The development comes as the president of Russia, Vladimir Putin, and his Ukrainian counterpart Petro Poroshenko were getting ready to meet on Tuesday in Belarus in the presence of EU foreign affairs chief.
The Facebook page for the Ukraine's anti-rebel operation, which includes the military, the national guard and interior ministry forces, said on Tuesday that the soldiers were from a Russian paratrooper division and were captured on Monday in the area of Amvrosiivka, near the Russian border in the Donetsk region.
The posting did not give details of how the capture took place. It posted videos of five men it said were among the captives, one of whom said the soldiers had been told they were being mobilised to take part in military exercises.
Russian news agencies quoted an unnamed source in the Russian defence ministry as saying that the soldiers were patrolling the border area and probably crossed the border inadvertently.
"The soldiers really did participate in a patrol of a section of the Russian-Ukrainian border, crossed it by accident on an unmarked section, and as far as we understand showed no resistance to the armed forces of Ukraine when they were detained," a source from Russia's defence ministry was quoted by Russian news agency RIA Novosti as saying on Tuesday.
The Ukrainian troops have been fighting pro-Russia rebels in the east of the country for around four months.
Kiev and the US have repeatedly accused Moscow of stoking the rebellion, but this is the first time Ukrainian authorities claimed to have taken captive soldiers from Russia's regular army.